The present invention relates to well logging tools and in particular to a logging tool for measuring formation resistivity known as the laterolog system. This is a device which utilizes a current injecting electrode on a sonde typically bracketed by current steering electrodes on the sonde which cause current to be steered radially outwardly from the sonde into adjacent formations. It is intended to measure formation resistivity of the formations immediately adjacent to a well borehole through which current flows.
The logging apparatus of this disclosure involves the injection of current radially outwardly from a sonde in a well borehole. The current flow is measured, and along with measurements of voltages at various locations on the sonde, a method of determining formation resistivity or its reciprocal which is conductivity is then obtained. Moreover, such devices provide a valuable indication of formation resistivity which resistivity values are regrettably interdependent on the geometry and uniformity of adjacent formations. If at a given instance the sonde positions such an electrode for injecting current radially outwardly into a formation which is extremely thick and relatively uniform in resistivity, then the measured resistivity of the formation is substantially accurate in view of the geometry of the formation. However, this is an ideal situation which does not always hold true. Consider the example of an interface between two large; or thick formations which have markedly different resistivity measurements. In the area of the interface, the resistivity measured for one formation will be modified by the resistivity of the adjacent formation. Consider another situation where the formations are quite thin, and there is therefore an interface above the current injection point and another interface below the current injection point. This then involves the formations which are above and below the formation immediately adjacent to the tool at which current is injected.
The adjacent formations have an impact on the data which is described generally as the shoulder bed effect, and the extent thereof depends on a number of parameters including the contrast between the resistivity of the surrounding beds, the distance along the well borehole from the current injection point to the respective beds above and below, the respective thicknesses of the formations or beds which are above and below, the diameter of the borehole, the conductivity of the fluid in the borehole, and other variables. In fact, because there are difficulties in sorting out these several variables, it has been the practice over the last few years to develop correction charts which take into account certain combinations of some, but not necessarily all of these parameters. As FIG. 1 of the drawings of the present disclosure will show, the borehole diameter and the ratio of resistivity between the borehole fluid and the shoulder beds are fixed variables for construction of that chart. The correction derived from the chart is carried out for a particular set of parameters fixed in accordance with the particular chart. This however requires separate charts to be computed for a large variety of combinations of hole diameter and the resistivity ratio. Even then, the charts are not totally effective. They are not effective because the ratios in the charts presume uniform and identical shoulders. The circumstances of the presumptions occur only rarely. The more common occurrence is that the formations are not uniform, and they may in fact be quite thin. Moreover, the shoulder beds above and below the current injection point may be similar but they may be radically different. The correction chart approach to reducing the number of variables is not totally effective.
The trade name SHOLAT identifies an algorithm which uses cumulative sequential resistivity steps, advancing a number of incremental steps, and provides a measure of simplification. With this simplification, there is a level of error derived from the basic assumptions. The assumptions are substantial and thus the inaccuracy of this approach becomes substantial in some circumstances.
In the present approach, certain assumptions are used which are more true to form. One of the first assumptions is that the log may be rectangularized. This requires that the advent of a particular zone or formation be observed and that assumed values be assigned to it which are uniform across that zone bed or formation. That assumption is thus applied to the full thickness of the particular bed.
In order to rectangularize the log, each given zone, bed, or formation, is assigned a uniform resistivity. This assigned resistivity is equal to the maximum measured resistivity in that zone if both adjacent zones (upper and lower) are less resistive. The assigned resistivity is equal to the minimum measured resistivity in that zone if both adjacent zones (upper and lower) are more resistive. Finally the assigned resistivity is equal to the average measured resistivity within the zone if one of the adjacent zones is more resistive and the other adjacent zone is more conductive.
Once the log is rectangularized, the response of the laterolog or other electrode tool is computed at the center of each zone using an exact computer model such as the Finite Element Model, or the Hybrid Method. A correction factor is then derived as the ratio of the assigned zone resistivity to the computed tool response. This correction factor takes into account the borehole fluid and diameter as well as the shoulder beds. In theory, further iterations should be performed whereby the shoulder bed resistivity is continuously replaced by the corrected value. In practice however, the process converges after only one or two iterations.
An important step of the presently disclosed method is simplification of more remote shoulder beds. For instance, if the current injection point, typically known as the measure point on the tool, is located at any particular instant, the beds which have the most impact are those that are within a specified vertical spacing. That vertical spacing can be arbitrarily defined as any particular range but it is a vertical distance of several feet. Sixty feet typically defines the region in which the formation resistivities have the most impact. Iterative processing in the rectangularization of the present data to obtain a match between the actual measurements and the iteratively processed data is a computing intensive protocol. The present method proposes to reduce the amount of processing by making simplifying assumptions for shoulder beds which are remote, that is those which are beyond the zone of interest which is arbitrarily defined in thickness. Accordingly, and again using the measure point on the tool, beds which are beyond 20 or perhaps 30 feet from the measure point can be collectively grouped and represented as a single value, and individual bed values are thus averaged. This cuts down on the number of beds required for computational purposes. Again and assuming a very simplistic example, assume that the measure point is at a particular location and beyond that measure point, there are a large number of beds located from 30 to 100 feet along the well borehole from the measure point. Those beds beyond 30 feet are grouped into an average value to reduce computational effort.
While the interface between adjacent formations of different resistivity may be located, the measured resistivity from a given formation may be in substantial error compared with the true resistivity of the formation as a result of the other formations. In other words, the absolute measure of resistivity may be in error, and the amount of error depends on the nature of the adjacent formations. In summary fashion, this error is dependent upon the contrast in the resistivity of the two formations. It also is dependent on the distance to the respective beds and their respective thicknesses. Another factor can be the diameter of the borehole and the conductivity of the drilling fluid that is in the well borehole. FIG. 1 of the drawings shows the borehole diameter and the resistivity ratio. A correction is carried out by entering the chart with the thickness measured for the bed of interest and the resistivity ratio of the shoulder bed. Quite obviously, this requires an individual chart for every combination of hole diameter and ratio of the respective resistivities. The trouble with the ratio determinations is that most of the ratios are derived from measurements involving highly monolithic, massive and identical strata so that the ratio aspect of the correction chart is idealized, and is therefore accurate only in unusual circumstance. Since shoulder beds are generally a sequence of several individual formations of mixed thicknesses and differing resistivities, the chart is idealized and incapable of dealing with the more common and practical aspects of the matter. Correction by means of a computer implemented algorithm SHOLAT was evaluated in the recent publication of Crary, et al, see "The Use of Electromagnetic Modeling to Validate Environmental Corrections for the Dual Laterolog" SPWLA Symposium Transactions, 1990.